General Relation between Fluxes from Collimated Point and Plane Sources of Radiation

Abstract

The radiation density (flux integrated over all directions) from a collimated point source is shown to be representable as a Fourier-Hankel transform of the density from a collimated plane oblique source. The spatial moments of a point-source density are similarly expressible as linear combinations of a finite number of moments of plane-source densities corresponding to different source obliquities. These results are valid for any type of radiation, provided that the medium is unbounded, homogeneous, and isotropic, and provided that a linear transport equation applies. The plane-geometry representation of densities and density-moments is equivalent to a "separation of variables." It allows one to solve a sequence of problems in one space variable (distance from a source plane) for different values of the source obliquity, and to use the information thus obtained for constructing the solution of a problem involving two space variables (e.g., the longitudinal and radial distances from a point source).